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Deconvolution of gas chromatographic data

The use of deconvolution methods on gas chromatographic data to obtain an accurate determination of the relative amounts of each material present by mathematically separating the merged peaks is discussed. Data were obtained on a gas chromatograph with a flame ionization detector. Chromatograms of five xylenes with differing degrees of separation were generated by varying the column temperature at selected rates. The merged peaks were then successfully separated by deconvolution. The concept of function continuation in the frequency domain was introduced in striving to reach the theoretical limit of accuracy, but proved to be only partially successful.

Howard, S.

Deconvolution of wide field-of-view radiometer measurements of earth-emitted radiation. II - Analysis of first year of Nimbus 6 ERB data

The theory of deconvolution considered by Smith and Green (1981) is applied to Nimbus 6 data in order to interpret the data with the maximum obtainable resolution. Attention is given to the data sample, sun-contaminated measurements, the measurement model, the deconvolution, the degree variance, the spherical harmonic coefficients, the geographical distribution of longwave radiation, time histories of zonal coefficients, and the effect of a grid system. Degree variance plots for 12 months of longwave radiation data show that the limit for a spherical harmonic representation of the Nimbus 6 wide field-of-view longwave data is 12th degree. The degree variance plots also reveal that most of the power is in the lower degree terms. Contour maps of the radiation field show the geographical distribution of earth emitted radiant exitance for each month.

Bess, T. D.

Thorium concentrations in the lunar surface. V - Deconvolution of the central highlands region

The distribution of thorium in the lunar central highlands measured from orbit by the Apollo 16 gamma-ray spectrometer is subjected to a deconvolution analysis to yield improved spatial resolution and contrast. Use of two overlapping data fields for complete coverage also provides a demonstration of the technique's ability to model concentrations several degrees beyond the data track. Deconvolution reveals an association between Th concentration and the Kant Plateau, Descartes Mountain and Cayley plains surface formations. The Kant Plateau and Descartes Mountains model with Th less than 1 part per million, which is typical of farside highlands but is infrequently seen over any other nearside highland portions of the Apollo 15 and 16 ground tracks. It is noted that, if the Cayley plains are the result of basin-forming impact ejecta, the distribution of Th concentration with longitude supports an origin from the Imbrium basin rather than the Nectaris or Orientale basins. Nectaris basin materials are found to have a Th concentration similar to that of the Descartes Mountains, evidence that the latter may have been emplaced as Nectaris basin impact deposits.

Metzger, A. E.

Achieving improved frequency response of the rain structure from spaceborne radar altimeters by employing deconvolution methods

A technique is described for arriving at improved measurements of the rain structure near the earth's surface from satellite-borne radars. The method uses deconvolution and Fourier transform procedures and assumes a knowledge of the antenna beam pattern. As an example, the method is directed toward the application of future spaceborne radar altimeters that may contain additional range gates to permit the measurement of rain in the lower troposphere. Using a radar-measured rain reflectivity profile acquired at Wallops Island, VA, in a simulation example, it is specifically demonstrated that improved measurements of the spatial frequency spectrum of the rain structure may be deduced by means of deconvolution methods, as compared to the measured spectrum derived by beam averaging. Rain measurements are considered vital from the standpoint of providing a flag for altimeter data that may be corrupted by rain. Such measurement capabilities should also provide sorely needed data on rain over the oceans where few or no such data are available for the meteorologist or the communicator interested in space diversity communications.

Goldhirsh, J.

Spatial deconvolution of IRAS galaxies at 60 UM

Using IRAS in a slow scan observing mode to increase the spatial sampling rate and a deconvolution analysis to increase the spatial resolution, several bright galaxies were resolved at 60 micron. Preliminary results for M 82, NGC 1068, NGC 3079 and NGC 2623 show partially resolved emission from 10 to 26 arcsec., full width at half maximum, and extended emission from 30 to 90 arcsec. from the center. In addition, the interacting system, Arp 82, along with Mark 231 and Arp 220 were studied using the program ADDSCAN to average all available survey mode observations. The Arp 82 system is well resolved after deconvolution and its brighter component is extended; the two most luminous objects are not resolved with an upper limit of 15 arcsec. for Arp 220.

Low, Frank J.

Punch stretching process monitoring using acoustic emission signal analysis. II - Application of frequency domain deconvolution

The coloring effect on the acoustic emission signal due to the frequency response of the data acquisition/processing instrumentation may bias the interpretation of AE signal characteristics. In this paper, a frequency domain deconvolution technique, which involves the identification of the instrumentation transfer functions and multiplication of the AE signal spectrum by the inverse of these system functions, has been carried out. In this way, the change in AE signal characteristics can be better interpreted as the result of the change in only the states of the process. Punch stretching process was used as an example to demonstrate the application of the technique. Results showed that, through the deconvolution, the frequency characteristics of AE signals generated during the stretching became more distinctive and can be more effectively used as tools for process monitoring.

Liang, Steven Y.

Response function of a tunable diode laser spectrometer from an iterative deconvolution procedure

A deconvolution procedure commonly used for resolution enhancement of spectra has been applied to the determination of the response function of a tunable diode laser spectrometer. The method is sufficiently fast and simple for routine application when correcting for nonnegligible instrumental broadening. Absolute linestrengths of CH4 in the 1327/cm region and line positions of HNO3 in the 1335/cm region, measured with the aid of the deconvolution technique, are reported here.

May, Randy D.

Laboratory for Engineering Man/Machine Systems (LEMS): System identification, model reduction and deconvolution filtering using Fourier based modulating signals and high order statistics

Several important problems in the fields of signal processing and model identification, such as system structure identification, frequency response determination, high order model reduction, high resolution frequency analysis, deconvolution filtering, and etc. Each of these topics involves a wide range of applications and has received considerable attention. Using the Fourier based sinusoidal modulating signals, it is shown that a discrete autoregressive model can be constructed for the least squares identification of continuous systems. Some identification algorithms are presented for both SISO and MIMO systems frequency response determination using only transient data. Also, several new schemes for model reduction were developed. Based upon the complex sinusoidal modulating signals, a parametric least squares algorithm for high resolution frequency estimation is proposed. Numerical examples show that the proposed algorithm gives better performance than the usual. Also, the problem was studied of deconvolution and parameter identification of a general noncausal nonminimum phase ARMA system driven by non-Gaussian stationary random processes. Algorithms are introduced for inverse cumulant estimation, both in the frequency domain via the FFT algorithms and in the domain via the least squares algorithm.

Pan, Jianqiang

A deconvolution technique for Hubble Space Telescope FGS fringe analysis

A technique has been developed for directly transforming interferometer fringe visibility functions ('S curves') from the Hubble Space Telescope (HST) fine guidance sensors (FGSs) into intensity profiles of the program object. In a process analogous to Fourier transform image deconvolution, an S curve from a double star yields a pair of narrow profiles containing information on the separation (in one coordinate), and relative brightness of the two stars. The procedure has yielded high internal precision for the separation and relative brightness in tests with HST data. Simulations indicate that it can also deconvolve S curves from multiple stars or continuous intensity distributions such as resolvable stellar or extragalactic objects. Similar deconvolution analyses may be useful in other types of interferometry.

Hershey, John L.

Minimum entropy deconvolution and blind equalisation

Relationships between minimum entropy deconvolution, developed primarily for geophysics applications, and blind equalization are pointed out. It is seen that a large class of existing blind equalization algorithms are directly related to the scale-invariant cost functions used in minimum entropy deconvolution. Thus the extensive analyses of these cost functions can be directly applied to blind equalization, including the important asymptotic results of Donoho.

Satorius, E. H.

Deconvolution of Hubble Space Telescope images using simulated point spread functions

Presented is a study of the use of simulated point spread functions (PSF's) to deconvolve Hubble Space Telescope images. We concentrate on images from the Wide Field and Planetary Camera (WFPC) and examine the affect of position dependence of the PSF and the telescope focus position on deconvolutions. Comparisons will be made to what will be expected from WFPC 2, which will include corrective optics. Since PSF's can be simulated for any specific observation, with the added advantage of being noise free and the ability to subsample them, they may be more suitable for deconvolution than observed ones in some cases. And since finding a suitable observed PSF may be difficult, simulated ones may be easier to use.

Krist, J. E.

DECONV-TOOL: An IDL based deconvolution software package

There are a variety of algorithms for deconvolution of blurred images, each having its own criteria or statistic to be optimized in order to estimate the original image data. Using the Interactive Data Language (IDL), we have implemented the Maximum Likelihood, Maximum Entropy, Maximum Residual Likelihood, and sigma-CLEAN algorithms in a unified environment called DeConv_Tool. Most of the algorithms have as their goal the optimization of statistics such as standard deviation and mean of residuals. Shannon entropy, log-likelihood, and chi-square of the residual auto-correlation are computed by DeConv_Tool for the purpose of determining the performance and convergence of any particular method and comparisons between methods. DeConv_Tool allows interactive monitoring of the statistics and the deconvolved image during computation. The final results, and optionally, the intermediate results, are stored in a structure convenient for comparison between methods and review of the deconvolution computation. The routines comprising DeConv_Tool are available via anonymous FTP through the IDL Astronomy User's Library.

Varosi, F.

Methods and Apparatus for Reducing Multipath Signal Error Using Deconvolution

A deconvolution approach to adaptive signal processing has been applied to the elimination of signal multipath errors as embodied in one preferred embodiment in a global positioning system receiver. The method and receiver of the present invention estimates then compensates for multipath effects in a comprehensive manner. Application of deconvolution, along with other adaptive identification and estimation techniques, results in completely novel GPS (Global Positioning System) receiver architecture.

Kumar, Rajendra

Deconvolution of Energy Spectra in the ATIC Experiment

The Advanced Thin Ionization Calorimeter (ATIC) balloon-borne experiment is designed to perform cosmic- ray elemental spectra measurements from below 100 GeV up to tens TeV for nuclei from hydrogen to iron. The instrument is composed of a silicon matrix detector followed by a carbon target, interleaved with scintillator tracking layers, and a segmented BGO calorimeter composed of 320 individual crystals totalling 18 radiation lengths, used to determine the particle energy. The technique for deconvolution of the energy spectra measured in the thin calorimeter is based on detailed simulations of the response of the ATIC instrument to different cosmic ray nuclei over a wide energy range. The method of deconvolution is described and energy spectrum of carbon obtained by this technique is presented.

Batkov, K. E.

An Optimal Deconvolution Method for Reconstructing Pneumatically Distorted Near-Field Sonic Boom Pressure Measurements

In-flight measurements of the SR-71 near-field sonic boom were obtained by an F-16XL airplane at flightpath separation distances from 40 to 740 ft. Twenty-two signatures were obtained from Mach 1.60 to Mach 1.84 and altitudes from 47,600 to 49,150 ft. The shock wave signatures were measured by the total and static sensors on the F-16XL noseboo. These near-field signature measurements were distorted by pneumatic attenuation in the pitot-static sensors and accounting for their effects using optimal deconvolution. Measurement system magnitude and phase characteristics were determined from ground-based step-response tests and extrapolated to flight conditions using analytical models. Deconvolution was implemented using Fourier transform methods. Comparisons of the shock wave signatures reconstructed from the total and static pressure data are presented. The good agreement achieved gives confidence of the quality of the reconstruction analysis. although originally developed to reconstruct the sonic boom signatures from SR-71 sonic boom flight tests, the methods presented here generally apply to other types of highly attenuated or distorted pneumatic measurements.

Whitmore, Stephen A.

Frequency-Domain Deconvolution for Flight Dynamics Applications

A deconvolution method is presented for estimating input data from measured output data and a model of the dynamic process involved. The method uses an optimal Wiener filter for separating the measured data into signal and noise components, and a high-accuracy Fourier transform for inverting the model dynamics in the frequency domain. The method is an extension of optimal Fourier smoothing, and uses a technique to enhance the contrast between the signal and noise spectra in designing the Wiener filter. The deconvolution method was applied to simulation and flight test data for the purposes of removing unwanted distortions introduced by signal-conditioning filters and sensor dynamics, and for reconstructing turbulence inputs from measured sensor data. Results indicated hat the method performs well given good signal-to-noise levels and accurate models of the dynamic process.

Grauer, Jared A.

Least-Squares Deconvolution of Compton Telescope Data with the Positivity Constraint

We describe a Direct Linear Algebraic Deconvolution (DLAD) approach to imaging of data from Compton gamma-ray telescopes. Imposition of the additional physical constraint, that all components of the model be non-negative, has been found to have a powerful effect in stabilizing the results, giving spatial resolution at or near the instrumental limit. A companion paper (Dixon et al. 1993) presents preliminary images of the Crab Nebula region using data from COMPTEL on the Compton Gamma-Ray Observatory.

COMPTEL